Consider the function g defined on [0,∞) by g(x)=x+x. The function is differentiable and strictly increasing on its domain, and thus possesses an inverse g−1.
(a) Show that the equation g(x)=3 has exactly one solution on [0,∞) and find that solution.
(b) Determine g−1′(3). Express your answer in exact form, not a decimal approximation.